We develop a rare chance-constrained optimal control framework for autonomous traffic management, with traffic dynamics governed by stochastic partial differential equations. To efficiently enforce these probabilistic safety specifications, we exploit a large deviation theory (LDT) based approximation method, which converts the original highly non-convex, sampling-heavy stochastic optimization problem into a tractable deterministic nonlinear programming problem. The proposed LDT-based reformulation exhibits superior computational scalability, as its computational cost remains approximately constant regardless of the target violation probability, as opposed to the scaling challenge of traditional sampling-based methods. The effectiveness of the proposed framework is illustrated through numerical experiments on a ring road with stochastic on-ramp inflow, and evaluated with two representative risk measures, namely, maximum traffic density and speed variation. The results show that the proposed method keeps the violation probability close to the target without parameter tuning and is more than ten times faster than a risk-averse baseline.

翻译：暂无翻译